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 ```I am building a portable trolley beam arrangement to move large stones in building a staircase. Most of the stones are around 1,500 lbs. Maximum load is 2,000 lbs which can, with the trolley, be in any position on the long beam. The trolley beam has a span of 13'. It rests on the center of another beam at each end (at right angles)which each have a span of 6'. The beams form an "I" in plan. I want to calculate the size of the beams required. I already own a 14' long 6x12 beam (4" wide, flat flanges} which I hope may be strong enough for the long beam, but if not, I could cut it for the two short beams, but because this is intended to be portable, I want to keep it as light as possible. I do have the option of adding another support to shorten the span if a particular stone is too heavy for my beams. If the 6x12 is two small for 2,000 lbs, can you tell me its capacity as a trolley beam? I would like to know what the safety factor is in such calculations and if the stone mason misjudges the load, and exceeds the "safe" limit, how much overloading is, in practical terms, expected before deforming the beams? (I want to be sure the stone mason is well informed.) In short: What beams should I use to move up to 2,000 lbs over a 13'span supported by 6' spans? How much weight could I support on a trolley with my 6x12, on a 13' span? Generally speaking, what percentage of load is required beyond the safe limits to deform the beams? Thank you, Joseph```
 ```Hello josephth, I think we can come up with a safe design for you. Safety factor for designs involving lifting of heavy loads are generally taken to be the ultimate strength of the material divided by six. A structural beam normally is considered to have an ultimate strength (Su) of 50,000 psi. This will give us a design stress of: Sd = Su/6 = 8,300 psi The reasons for such a large safety factor are that design loads are often exceeded, devices may be damaged, and large shock loads may occur due to rigging slips or failure. In designing a beam either the bending moment or the allowable deflection rules. Generally in short beams (such as both of yours) deflection is not a concern. I checked deflection just to make sure and it does not affect beam selection in your design. So, I will not include those calcs just to make things as simple as possible. 6' beam design: We can take the worst case where the trolley is adjacent to one of the end beams and assume that the 2,000# is fully applied at the center of the beam. The maximum bending moment (M) is: M = P x l/4 = 2,000# x 72 in. / 4 = 36,000 in-lb The required section modulus (S) is: S = M/Sd = 36,000 / 8,300 = 4.33 in^3 13' beam design: The worst case here is when the trolley is at the center of the beam. So, we have: M = Pl/4 = 2,000# x 156 in. / 4 = 78,000 in-lb S = M/Sd = 78,000 / 8,300 = 9.39 in^3 The section modulus of your W6x12 beam is 7.25 in^3. It would be fine for the 6' beams. The 13' span beam requires a beam with a section modulus at least 9.39 in^3. A good choice would be a W6x16 with a value of 10.2 in^3. If you have any questions after reading this, please ask for a clarification and I will be glad to explain further. Good luck with your stone work, Redhoss```